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Homeomorphisms of Locally Finite Graphs

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Abstract

In this paper, we show that every pointwise recurrent homeomorphism of a locally finite graph is regular. We also give some qualitative properties of an equicontinuous group of homeomorphisms of a finite graph.

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Notes

  1. A decomposition of E is a partition of E by nonempty closed pairwise disjoint subsets. Let D be a decomposition of E. For \(x\in E\), let D(x) denote the element of D containing x. The decomposition D is said to be continuous provided that if \((x_n)\) is a sequence which converges to \(x_0\), then

    $$\begin{aligned} D(x_0)\subset \liminf {D(x_n)}\subset \limsup {D(x_n)} \subset D(x_0) \end{aligned}$$

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Authors and Affiliations

  1. Laboratoire des Systèmes Dynamiques et Combinatoires, Faculté des Sciences de Sfax, Sfax, Tunisia

    Hawete Hattab & Ezzeddine Salhi

  2. Umm Al-Qura University, Makkah, Kingdom of Saudi Arabia

    Hawete Hattab

Authors
  1. Hawete Hattab
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  2. Ezzeddine Salhi
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Correspondence to Hawete Hattab.

Additional information

This work is supported by the laboratory of research “Dynamical systems and combinatorics” University of Sfax, Tunisia.

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Hattab, H., Salhi, E. Homeomorphisms of Locally Finite Graphs. Qual. Theory Dyn. Syst. 15, 481–490 (2016). https://doi.org/10.1007/s12346-015-0182-8

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